Method for production of cellulose and hemicellulose fibers from lignocellulose biomass obtained from sugarcane leaves and buds by applying a process comprising the stages of: a) Diminishing the particle size of the lignocellulose biomass to a range between 3 and 15 mm, b) Subjecting the product obtained to treatment with one or more solvents and/or a mixture of specific catalysts, c) Carry out sudden decompression to an atmospheric pressure, d) Collecting the pretreated material in a cyclone, e) Optionally separating the liquid and solid fractions through washing and filterung f) Optionally, treating the solid fraction in a reactor with a mixture of ethanol and chlorine dioxide, d) Wash the product obtained to achieve cellulose efficiency above 50% and of lignin of 5 to 7%, fiber lengtht in a range to 1,5 to 2,7 mm, breaking length (km) of 7,0 -8,9, Burst index (kPam2/g) of 4,5-7,2 and Tear index (mNm2/g) of 8,2-8, The obtained high-resistance cellulose and hemicellulose is especially suitable for the paper production and polymer-type plastics.